Molecular Dynamics Simulation of the Aggregation … › files › publications › 2015 › ...Molecular Dynamics Simulation of the Aggregation Patterns in Aqueous Solutions of Bile

Molecular Dynamics Simulation of the Aggregation Patterns inAqueous Solutions of Bile Salts at Physiological ConditionsFatmegyul Mustan,† Anela Ivanova,*,‡ Galia Madjarova,‡ Slavka Tcholakova,† and Nikolai Denkov†

†Department of Chemical and Pharmaceutical Engineering, and ‡Department of Physical Chemistry, Faculty of Chemistry andPharmacy, University of Sofia, 1 James Bourchier Avenue, 1164 Sofia, Bulgaria

*S Supporting Information

ABSTRACT: Classical molecular dynamics simulations areemployed to monitor the aggregation behavior of six bile salts(nonconjugated and glycine- and taurine-conjugated sodiumcholate and sodium deoxycholate) with concentration of 10mM in aqueous solution in the presence of 120 mM NaCl.There are 150 ns trajectories generated to characterize thesystems. The largest stable aggregates are analyzed todetermine their shape, size, and stabilizing forces. It is foundthat the aggregation is a hierarchical process and that itskinetics depends both on the number of hydroxyl groups inthe steroid part of the molecules and on the type of conjugation. The micelles of all salts are similar in shape−deformed spheresor ellipsoids, which are stabilized by hydrophobic forces, acting between the steroid rings. The differences in the aggregationkinetics of the various conjugates are rationalized by the affinity for hydrogen bond formation for the glycine-modified salts or bythe longer time needed to achieve optimum packing for the tauro derivatives. Evidence is provided for the hypothesis from theliterature that the entirely hydrophobic core of all aggregates and the enhanced dynamics of the molecules therein should beamong the prerequisites for their pronounced solubilization capacity for hydrophobic substances in vivo.

■ INTRODUCTION

Bile acids (BAs) are bioactive compounds synthesized fromcholesterol in the liver. Most of them, bound to glycine ortaurine residues, are ionic along the gastrointestinal tract. Oneof the most important BA specifics is the formation ofaggregates, which solubilize the hydrophobic products of theenzymatic hydrolysis of triglycerides upon digestion in thegastrointestinal tract and facilitate their metabolism. Due totheir vast practical significance BA aggregates have beenintensively studied experimentally. The most frequently usedmethods for determination of the aggregates’ size are laser lightscattering, small-angle neutron scattering, proton NMR, andcryogenic transmission electron microscopy (cryo-TEM).1,2

Small and co-workers3 investigated the aggregation numbers(Nagg) of bile salts (BS) by ultracentrifugation and by laser lightscattering. They discovered that all trihydroxy bile salts formvery small micelles with Nagg < 10, which are resistant tochanges in counterion concentration or temperature. Dihy-droxy BS formed small micelles at low concentration (aroundthe critical micelle concentration, CMC) and large micelles(Nagg = 12−100) at higher concentration (well above theCMC). A temperature increase resulted in a significant decreasein the micelle aggregation number. It was shown that pH hadmild effect on Nagg of the trihydroxy derivatives while the size ofthe dihydroxy aggregates increased upon pH lowering down tovalues around pKa of the bile acids.A convention exists in the literature to denote the smaller

micelles as primary and the larger ones as secondary.3 It is

believed that primary micelles typically assemble via hydro-phobic forces,4 and their aggregation numbers vary in the range2−9 molecules. Secondary micelles are formed by hydrogenbonding of the primary ones, and their Nagg values span a muchwider range. According to Small and co-workers,3 onlydihydroxy BS can yield secondary micelles whereas thetrihydroxy ones assemble predominantly into primary micelles.The aggregation of taurine-conjugated cholate (TCH,

trihydroxy BA) and deoxycholate (TDCH, dihydroxy BA)was studied experimentally to determine Nagg and the radius ofthe micelles. The latter was measured by ultracentrifugation, gelfiltration, and free diffusion.5−7 For TDCH with concentrationsslightly above CMC in aqueous solution with 150 mM NaCl at20 °C, Nagg was 18, which indicated the formation of secondarymicelles. Their apparent radius was between 2 and 2.4 nm. ForTCH in the same concentration range and at identical ionicstrength but at 37 °C, Nagg was 5, and the radius was ca. 1 nm.More recent reports of various authors8−14 confirmed the

exceptionally small aggregation number of bile salts 2 ≤ Nagg ≤15 (in aqueous solution with 150 mM NaCl, pH 7, roomtemperature). It was shown that Nagg depends on the type ofthe surfactant, nonconjugated or glycine- or taurine-conjugated,as well as on the number, orientation, and position of hydroxylgroups in the steroid ring. It was established also that

Received: July 22, 2015Revised: November 16, 2015Published: November 25, 2015

Article

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© 2015 American Chemical Society 15631 DOI: 10.1021/acs.jpcb.5b07063J. Phys. Chem. B 2015, 119, 15631−15643

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http://dx.doi.org/10.1021/acs.jpcb.5b07063

deoxycholates had larger Nagg than cholates and that tauro-conjugates formed smaller micelles than glyco-derivatives.None of these studies, however, reported exact structures andsizes of the micelles. It was stated only that the aggregates werevery dynamic and flexible.There are also theoretical communications in the literature,

addressing the aggregation process of BS mostly by moleculardynamics (MD) simulations. Partay et al.15 studied thebehavior of aqueous solutions of sodium cholate (CH) anddeoxycholate (DCH) at three concentrations: 30, 90, and 300mM. Parameters based on the classical force field GROMOS87were used for the bile salts and for the ions, while the modelSPC/E was employed for water. All systems were simulated atroom temperature. It was found that the two salts formed onlyoligomers at the lowest concentration, which is closest to thephysiological concentration, determined in vivo in humans.Those of DCH were stabilized by hydrophobic attraction forcesbetween the steroid rings. For CH aggregates, intermolecularhydrogen bonding was reported in addition to the hydrophobicinteractions. Nagg for cholate was 4.5 and for deoxycholate −4.1,the largest aggregates of the two BS being pentamers andhexamers, respectively. At the highest studied concentration,the molecules formed secondary micelles, which were stabilizedby hydrophobic interactions and hydrogen bonds. An aggregatesize of 30−40 molecules was reported. It was concluded thatthe secondary micelles of DCH were formed by hydrogenbonding of smaller hydrophobically stabilized primary micelles.On the contrary, the secondary micelles of CH resulted fromhydrophobic attraction of hydrophobically or H-bonded smallclusters.

The same authors showed16 that the molecular structure ofbile salts, which differs considerably from that of conventionalsurfactants, is the reason for obtaining micelles of variousshapes: ellipsoid or rod-like. It was observed that the preferredmolecular orientation within the micelles is with parallel steroidparts of the neighboring molecules. Spherical primary micelleswere reported for DCH while CH assembled into disc-like orellipsoid shapes.Similar aggregate shapes were observed by Warren et al.17

who simulated by MD the aggregation of six bile salts: cholate,glycocholate (GCH), taurocholate, glycochenodeoxycholate,glycodeoxycholate (GDCH), and glycolithocholate in aqueoussolution with concentration of ∼100 mM. Nagg varied between8 and 17. The obtained results showed that the shape of themicelles ranges from deformed sphere to elongated structures,in which the molecules face their steroid rings. The authorsconcluded that intermolecular hydrogen bonds were the mainfactor influencing the size, structure, and dynamics of themicelles.Verde et al.18 performed coarse-grained MD simulations of

different bile salts in implicit solvent and found small micelleswith close to spherical shape and larger, more elongated onesfor two types of BS (with two and three hydroxyl groups). Theanalysis of micelle formation of these two molecules and of ahypothetical derivative without hydroxyl groups revealed thatthe trihydroxy modification formed smaller micelles than thedihydroxy one at a given concentration, while the hypotheticalmolecule gave the largest aggregates. Since hydrogen bondswere not taken into account in these simulations, while micellesformed regardless of that, the authors assumed that hydrogenbonding was not essential for formation of the small micelles

Figure 1. Chemical structures of the bile salts most abundant in the human organism, which are studied in the present work. The abbreviations ofeach molecule used throughout the text are denoted.

The Journal of Physical Chemistry B Article

DOI: 10.1021/acs.jpcb.5b07063J. Phys. Chem. B 2015, 119, 15631−15643

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and that they were stabilized by hydrophobic forces. Theauthors suggested also that the profound dynamics of themolecules within the micelles had physiological relevance forthe formation of mixed micelles with lipophilic substances fromthe gastrointestinal tract.A survey of the literature showed no theoretical reports on

the kinetics of bile salt aggregation at concentrations close tothe physiological conditions in vivo, i.e., about 10 mM, in spiteof the known fact that the aggregation of these compoundsdepends strongly on their bulk concentration.3 The abovesynopsis also indicates that there is no unified opinion on thenature of the driving force for aggregation of BS in aqueoussolution. Hence, the aims of the present study are 2-fold: (1) tomonitor the kinetics of aggregation of 6 bile salts (non-conjugated and glycine- and taurine-conjugated cholate anddeoxycholate, respectively; see Figure 1) in aqueous solutionwith bile concentration of 10 mM in the presence of 120 mMNaCl at 37 °C and to elucidate the interactions influencing therate of aggregates formation, (2) to analyze the intermolecularforces acting within the most stable aggregates and definingtheir shape and size, and how these interactions are affected bythe conjugation in the hydrophilic head of the molecules and bythe number of hydroxyl groups in the steroid fragment.The ultimate goal of the study is to reveal the factors defining

the solubilization capacity of BA micelles for hydrophobic

substances such as cholesterol, products of triglycerideshydrolysis, and pharmaceutics, at conditions mimicking thosein the human gastrointestinal tract. The present work can beregarded as the first step in this direction.

■ MOLECULAR MODELS AND COMPUTATIONALPROTOCOL

The setup of the virtual experiment was aimed to reproduce asmuch as possible, within the limitations of the method, realexperimental conditions19 which mimic the situation in vivo.The concentration of bile salts in the aqueous solution model is10 mM, and that of NaCl is 120 mM. These concentrationscorrespond to 8 molecules of bile anions neutralized by 8sodium cations in each simulation box with edge length 11 nm.All boxes are cubic, and each of them contains also 112 Na+,112 Cl−, and ca. 43 600 water molecules, which result in totalvolume of each model system of 1.331 × 10−24 m3 (see FigureS1 of the Supporting Information for illustration). Periodicboundary conditions are applied in the three directionsthroughout the simulations to model continuous solutions. Inthe initial configurations all ions are placed randomly in thesimulation boxes and are then left to self-assemble during theMD runs.The force field AMBER9920,21 is used for all ions, while the

model TIP3P22 is employed for the water molecules. Since

Figure 2. Evolution of the maximum cluster size of the six studied systems during the MD simulations.



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AMBER does not contain parameters for the sulfate fragmentof taurine, the necessary values are adopted from Gaff (TableS1).23 The atomic charges of the BS needed to calculate theelectrostatic contribution to the energy are derived by applyingthe RESP procedure24,25 where the charges are fit to thequantum mechanical electrostatic potential of each molecule,generated at the HF/6-31G* level for geometries of themolecules optimized with the DFT functional B3LYP26−29 andbasis set 6-31G*30 within the program package Gaussian09.31

The final RESP charges (Tables S2.1 and S2.2 and Figure S2 inthe Supporting Information) are averaged over the most stableconformers of each molecule. The atom types of all atoms arealso provided in the Supporting Information (Table S3).The following computational procedure is applied to all

studied systems: energy minimization of the initial config-uration, heating to 310 K, relaxation for 0.5 ns, and productionruns with length 150 ns. The time step is 2 fs. All MDsimulations are done in NVT ensemble to comply with thedesired concentration. Constant temperature is maintainedwith the Berendsen thermostat32 with coupling constant of 0.1ps. The algorithm leapfrog is used to integrate the equations ofmotion. The lengths of all hydrogen-containing bonds are fixedwith SETTLE33 (for the water molecules) and LINCS34 (forthe bile salts). The Lennard-Jones potential is truncated at 10 Åwith a switch function turned on at 8 Å. Electrostaticinteractions are evaluated in the monopole approximationwith the method PME;35−37 the cutoff for the direct part of thesum is 12 Å with a switch function initiated at 10 Å.Equilibration of the systems is verified by monitoring theevolution of the total energy and temperature, and of thetemperatures of the separate components. The RMSD variationof the BS atomic coordinates with time is selected as astructural criterion. All these parameters fluctuate aroundconstant average values during the production runs, whichconfirms that thermodynamic equilibrium has been attained.However, the bile salt aggregates are analyzed only after theself-assembly process of each system has reached the stationarystate (see Figure 2 and discussion in the text).The production trajectories are subject to statistical analysis

including snapshots separated by 1 ps. The entire productionstage of 150 ns is used only to monitor the kinetics ofaggregation. The properties of the most stable aggregates (seebelow) are obtained by processing only the part of the MDtrajectories where they exist (Table 1). The program packageGROMACS 4.5.238 is used for all simulations and for analysis.VMD39 is employed for visualization of the trajectories.

The kinetics of aggregation is followed by cluster analysis,carried out with the method of single linkage, which usessimilarity of atomic coordinates to assign molecules to anaggregate. The cutoff, which has the meaning of the largestinteratomic distance between the closest atoms of neighboringmolecules in a cluster, is taken as the end of the first peak of theminimum distances distributions (see below). This analysisyielded a value 0.28 nm, which is employed as a limitingdistance when determining cluster sizes. Notably, it coincideswith the full width at half-maximum of the radial distributionfunction (RDF) between the centers of mass of neighboring BSmolecules within stable dimers, which agrees with the findingsfrom a very detailed general analysis of RDFs.40

■ RESULTS AND DISCUSSIONThe aggregation behavior of the studied molecules is comparedby estimating the times necessary for the formation of thelargest aggregates within the model, their persistence in time,and the nature of the forces acting between the molecules.Representative aggregates of each BS are analyzed in moredetail to calculate their size, shape, and type of stabilizingintermolecular interactions.

Cluster Analysis: Aggregation Numbers and Kineticsof Formation. The evolution of the size of the largest clusterfor all BS is shown in Figure 2. It reveals a systematic increaseof the aggregates’ size with time. Only for CH and TDCH alarger cluster dissociates temporarily to a smaller one (apentamer to a tetramer) but is restored in ca. 20 ns. For thetime of the simulations the nonconjugated salts and the tauroconjugates form stable pentamers while the glyco derivativesyield a hexamer (GCH) and an octamer (GDCH). The timerequired to form a stable pentamer is the shortest for TDCH (6ns) and the longest for TCH (109 ns). CH and DCH aggregatewithin intermediate times: 48 and 87 ns, respectively. GCHassembles into a stable hexamer for 31 ns, and this is the onlysystem for which no long-living pentamer is registered. Thestable octamer of GDCH is formed for 77 ns. Both types ofconjugated molecules (tauro and glyco) aggregate faster thanthe nonconjugated ones. It should be noted that all kineticsresults should be interpreted in a qualitative manner as relativedata for the different salts. The numbers provided above can beabsolute quantitative indicators only if they stem from a largenumber of NVT MD simulations for each system, which ishardly plausible at the current state of computational power.Nevertheless, they reflect appropriately the aggregationspecificity of the various bile salts.Increase of the aggregates’ size takes place by gradual

addition of monomers to the largest micelle already formed andnot by merging of smaller clusters. For a very short time(during the relaxation or shortly after that) the initiallyrandomly placed BS molecules self-assemble into dimers,which are very dynamic and frequently exchange moleculeswith the bulk. The dimer of TDCH is the only exception: onceformed, it persists for about 6 ns when three more moleculesassociate to it to give a pentamer.To reveal the reason for this pronounced stability of the

TDCH dimer, the properties of dimers of the six BS, whichwere stable for 996 ps in the initial phase of the simulations(the first 4 ns), were analyzed. The number of contacts and theminimum interatomic distance (within a cutoff of 0.30 nm)between atoms of the two molecules in each dimer for thewhole period were determined first. The results are summarizedin Figure 3. It is evident that the atoms in the TDCH dimer are

Table 1. Summarized Data for Calculated and ExperimentalAggregation Numbers (Nagg’s), Moments of Formation (τf),and Relative Populationa of the Most Stable Aggregates ofthe Six Studied Bile Salts

molecule Naggcalc Nagg

exp τf, ns population, %

CH 5 4.8 48.3 57.8DCH 5 13.3 86.5 39.7GCH 6 5.6 31.3 78.9GDCH 8 16.2 77.0 48.7TCH 5 4.5 108.9 27.4TDCH 5 18.0 6.4 79.0

aObtained as the ratio of the time during which a given cluster existsto the entire time of the simulation.



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at much shorter distances than those in the other dimers, whichnaturally results in a much higher number of contacts.Moreover, the distribution of the number of contacts there ismuch broader than in the other systems indicating that a largernumber of favorable orientations of the two molecules exist inthe TDCH dimer. The average number of contacts in thisdimer is ≈24, for GCH it is ≈16, and for the rest of the dimersit is between 11 and 13. The difference for the dimers of TCHand TDCH is twice (12 vs 24 contacts), even though the twomolecules differ in one hydroxyl group only.Next, the most probable relative orientation of the two

molecules within the dimers was estimated. A vector shown inFigure 4A was defined for each molecule. It was chosen becauseit connects the two outermost atoms of the steroid fragment,which is an identical rigid part of all molecules. The variation ofthe angle between the vectors of the two molecules for theperiod of stability of the dimers of TCH and TDCH ispresented in Figure 4B.This analysis reveals that up to 200 ps the most probable

angle between the two TCH or TDCH molecules is about155°. After that a conformational transition takes place leadingto a decrease of the angle to ca. 70° for TCH and to ca. 10° forTDCH. After 400 ps the angle in the TCH dimer is restored toabout 155° and fluctuates around this value until the separationof the two molecules. On the contrary, the angle in the TDCHdimer relaxes to about 35° and varies around this magnitude(Figure 4B). To provide an explanation for this contrastingbehavior, the intermolecular hydrogen bonds in the dimers ofTCH and TDCH were analyzed. It was found that there ispractically no H-bonding in the former whereas two hydrogenbonds (denoted in Figure S3 of the Supporting Information)exist in the dimer of TDCH for 65% of the trajectory (996 ps)of this dimer. Therefore, the dimer of TDCH owes its stabilityto these two intermolecular hydrogen bonds. The moreresistant dimer of TDCH leads to faster aggregation up to astable pentamer within 6 ns.

In contrast, in the dimer of TCH the molecules interact onlythrough their hydrophobic steroid rings, which renders theirseparation easier. Breaking this dimer is facilitated further bythe pronounced hydrophilicity of TCH. Due to this, a stablepentamer of the taurocholate is formed only after 100 ns, andthe molecular behavior therein is different from that in thepentamers of the other BS. The main difference stems againfrom the number of intermolecular contacts in the aggregates,which is much smaller for TCH, as discussed below (Table 3).Trimers are not abundant in any of the studied systems,

which is seen from the size distribution of the aggregates shownin Figure 5. Tetramers are also short-lived (except for TCH).This is due to the fact that 3 or 4 molecules are not sufficient

Figure 3. (A, B) Minimum distances per picosecond and (C, D) number of atomic contacts per picosecond between the molecules in the dimersformed at the beginning of the simulations by the six bile salts.

Figure 4. (A) Illustration of the vector used to assess theintermolecular orientation of BS in the aggregates. (B) Evolution ofthe angle formed between the vectors of the two molecules in a dimerof TCH (black) and TDCH (red) for a period of 996 ps.



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for efficient packing of all hydrophobic parts away from thewater molecules. The tetramer of TCH is relatively stablebecause this molecule has the largest hydrophilic surface area,and four molecules are sufficient to shield the hydrophobicfragments. They survive for ca. 60 ns, and then a pentamerforms, which remains stable until the end of the simulation.This result is in very good agreement with literature data3

providing an aggregation number of 4.5 for TCH.In almost all systems studied the largest aggregates formed

are also the longest-living. The exceptions are the non-conjugated molecules, for which monomers are the mostpopulated due to their generally slower self-assembly. Never-theless, intensive dynamics and stepwise increase of the size ofthe aggregates is witnessed for all BS. Since the aggregationcould in principle depend on the choice of the thermodynamicensemble, we have run also a 100 ns NPT simulation (atpressure of 1 bar and the same temperature as in the NVTcalculation) for one of the studied systems, the solution ofTDCH. Some key results are summarized in Figures S4 and S5of the Supporting Information. Both in NVT and in NPT themolecules of TDCH aggregate stepwise and reach a stablepentamer and hexamer, respectively. As could be expected, theinitial times of formation of the pentamer are different in thetwo trajectories, but nevertheless, it assembles quite fast (at ca.23 ns) in the NPT simulation as well. In both simulations thelargest population belongs to the largest cluster formed and thesmallest one to a trimer (Figure S4B). The overall distributionsare alike, too. Analysis performed for the pentamers from thetwo simulations shows very similar hydrogen bonding anddispersion interaction patterns (Figure S5). So, it is assumedthat the influence of the ensemble is small.Unlike the nonconjugated salts and the tauro conjugates,

which form stable pentamers, the glyco derivatives yield

aggregates of larger size: a hexamer for GCH and an octamerfor GDCH. GCH is the only salt without a stable pentamer. Ina very short time a hexamer is formed, which perseveres untilthe end of the simulation. This indicates that more than fiveGCH molecules need to pack in order to provide anenergetically favorable configuration. The necessity of a largernumber of molecules probably comes from the larger size ofthis ion compared to the nonconjugated one and from thesmaller hydrophilic head compared to the tauro derivatives.The participation of the hydrophilic head of GCH into theaggregation process is addressed in more detail below. In theGDCH models the molecules gradually group to grow to atrimer (Figure 2), a tetramer, a pentamer, and a heptamerwithin 77 ns, after which a stable octamer forms persisting for73 ns until the end of the simulation. It cannot be claimed that8 is the aggregation number of GDCH because of the limitationof the model, but this is the only system where the maximumpossible cluster size is reached, which is in an agreement withthe experimental data by Small and co-workers,3 who obtainedthe largest Nagg for this system as well (Table 1).The tendency for the nonconjugated salts resembles that of

the glyco conjugates. Both CH and DCH form stablepentamers. DCH indicates a possibility for aggregation into alarger cluster, a hexamer, which exists during the last 2 ns of thesimulation.The aggregation numbers observed within the current

models are 5 for CH and TCH and 6 for GCH. DCH andTDCH also form stable pentamers, and GDCH, an octamer.The results obtained for the trihydroxy derivatives agree verywell with experimentally determined Nagg known in theliterature (Table 1). The aggregation numbers of the dihydroxyrepresentatives found in the present work, however, are muchsmaller than those derived from experimental data. This may be

Figure 5. Histograms of cluster size normalized for 150 ns of simulation showing the relative population of the BS molecules in aggregates withdifferent size. The plot on the left is a comparison of the trihydroxy salts, and that on the right is of the respective dihydroxy derivatives.

Figure 6. Comparison of the kinetics of micelles formation of the studied bile salts as a function of the number of hydroxyl groups (left vs right) andof the type of hydrophilic head (colors).



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interpreted as more pronounced affinity of the dihydroxy BStoward formation of secondary micelles. It should be noted thataggregation numbers cannot be determined unambiguouslywithin this study since the simulations are stopped at 150 ns.Another limiting factor is the size of the models, each of whichcontains 8 BS molecules only. Investigation of the largerpossible aggregation numbers is planned in the next stage of thestudy by coarse-grained MD. Here, mostly relative numbers arediscussed, and when absolute values are given, they should beregarded within the limitations of the model.The influence of the number of hydroxyl groups on the size

of the aggregates and on the rate of aggregation is illustrated inFigure 6 where the symbols denote the moment of formation ofthe clusters with different size. Although the dihydroxy salts arecharacterized with higher Nagg, their aggregation appears slowerthan that of the trihydroxy molecules in the nonconjugated andin the glyco derivatives. The tauro conjugates deviate from thistrend since TCH self-assembles comparatively slowly andTDCH has the fastest aggregation among all studied systems.This mismatch of the kinetic trends between the di- andtrihydroxy salts might stem from the initial random placementof the molecules in the periodic box. In order to eliminate theinfluence of the starting structure during the initial stage of theaggregation, 20 ns simulations were carried out for all bile saltsusing identical starting configurations. The results aresummarized in Figure S6 of the Supporting Information. Theprofiles do not differ much from the first 20 ns in Figure 2, buta more uniform trend is witnessed. The micelles of TDCH andGDCH grow faster than those of TCH and GCH. Thisindicates speedier self-assembly of the dihydroxy conjugates.Only dimers of CH and DCH exist during these simulations,which reflects their slower aggregation kinetics. Inspection ofthe dimers confirmed the conclusion made above, that thedimers of TCH are very mobile while in TDCH a fixedorientation prevails. Hence, it can be assumed that thisalignment is preferential for faster aggregation.However, dominant intermolecular alignment is not retained

in the larger stable clusters. There is no fixed relativeorientation of the molecules within the micelles. Expectedly,the most frequent alignment of neighboring molecules is facingthe hydrophobic parts of their steroid rings, which correspondsto literature data from other theoretical studies.16−18 This isseen most clearly in the dimers (Figure S3, right). In most ofthe dimers the methyl groups of the two molecules aresomewhat displaced, and the hydrophilic heads are solvated bywater molecules. This preferred orientation can be explained bythe fact that the heads are negatively charged, and hence, theirface-to-face orientation is electrostatically unfavorable. In thelarger clusters of all BS the hydrophilic heads remain locatedprimarily at the periphery of the micelle, pointing toward water,which corroborates their enhanced hydrophilic nature. Thiscasts some doubt on the possibility for formation ofintermolecular hydrogen bonds within the clusters, whichsome literature sources3,15,41 delineate as the main reason forstabilization of BS micelles. Detailed analysis of H-bonding ispresented in the next section.It should be noted, however, that no orientational ordering of

the molecules takes place within the aggregates (Figure 7).Neighbors can close different angles with each other. This isconfirmed by analysis of the angle between the vectors definedlongitudinally for each molecule within a given aggregate(Figure 4). The evolution of this angle is monitored for all pairsof molecules, and it spans the entire range from 0° to 180° (a

representative example is shown in Figure S7 of the SupportingInformation). This means that there is no preferredintermolecular orientation in any of the micelles and impliesthat the BS micelles could easily rearrange their structure inorder to host suitable hydrophobic hosts such as cholesterol.In order to characterize the type of interactions between the

BS molecules within the aggregates, the most stable clusters ofthe six salts were compared for identical period of time, 30 ns,selected as the optimum time during which a stable micelleexists in all systems. For correct comparison, all quantities(number and length of hydrogen bonds, number and length ofintermolecular distances describing hydrophobic interactions)are calculated for the entire cluster and then normalized for onemolecule.

Hydrogen Bonds. Intermolecular hydrogen bonds betweenBS in their aggregates are discussed extensively in theliterature3,15,41 as one of the main driving forces stabilizingthe micelles. The presence of several hydroxyl groups (2 or 3)and a carboxyl, glycyl, or tauryl residue in these moleculesenables formation of hydrogen bonds, which may stabilize theclusters.Therefore, the hydrogen bonds within each representative

aggregate of the six studied BS were evaluated. The H-bondsbetween BS and water molecules were calculated, too. Aproton/H-acceptor cutoff = 0.35 nm and maximum limitingangle proton/H-donor/H-acceptor of 30° were used. Distribu-tions of the number of hydrogen bonds between BS moleculeswithin the clusters are given in Figure 8, and the averagenumber of H-bonds of BS with water is summarized in Table 2.It is seen that the most probable number of H-bonds

between BS molecules is small: formation of 1 or 2 hydrogenbonds is the most likely (2 or 3 for GDCH). However, themaximum probability per molecule is around 7% for the tauroderivatives and much less for the other molecules in spite of thefact that each of them contains at least 4 electronegative atoms,which may bind some of the available protons (minimum 2).This negligible affinity toward hydrogen bonding inside theclusters can be rationalized in terms of the micelles’ structure:the molecules turn preferably their hydrophilic parts towardwater aiming to shield as much as possible the hydrophobicfractions from it (Figure 9).Hydrogen bonds between the molecules of cholate and

deoxycholate will not be discussed because their average

Figure 7. Illustration of the most populated clusters of all BS:pentamers of CH, DCH, TCH, and TDCH; hexamer of GCH; andoctamer of GDCH.



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number for the entire pentamers is less than 0.1 (Table 2), andtherefore, we assume that H-bonding is negligible in thesemicelles. This conclusion contradicts the statement by Partay etal.15 that hydrogen bonding is significant in the primarymicelles of cholate.There might be several reasons for this discrepancy. First, the

different force field/water model combinations (united-atomwith SPC/E in the study of Partay et al. vs all-atom with TIP3Pin the current work) are likely to result in different balance ofthe nonbonded interactions. This is confirmed by a recentdetailed comparative study of the two types of force fields forthe description of a surfactant micelle.42 There, AMBER99SBand the newer versions of GROMOS are shown to reflectadequately the micellar properties. Second, Partay andcoauthors15 use distance criteria for hydrogen bonding. This

assumption takes into account only implicitly the angularcomponent of H-bonds, which exists in the official definition.43

Hence, the H-bonding criterion in the current study issomewhat more stringent. It should also be mentioned thattheir simulations are carried out at room temperature where thedynamics of molecules is slower and more H-bonds could bestabilized. Last but not least, the simulation times of Partay etal. are much shorter, and given the slower aggregation withGROMOS,42 and the fact that H-bonds were observedpredominantly in cholate dimers, this may well be a reflectionof the earlier stages of CH self-assembly. To test this, theintermolecular hydrogen bonds were calculated within a CHdimer existing in the period 13.5−29.0 ns in our trajectory. H-bonds were seen to form and break occasionally, with theiraverage number being 0.03 ± 0.22, which is in the rangereported by Partay et al. All this indicates that the negligiblehydrogen bonding in the most stable micelles of CH and DCHregistered in the present work is realistic for the conditionsstudied herein. Apart from H-bonding, the two studies agreequite well in terms of aggregates’ size and relative behavior ofCH and DCH.The distribution of the number of H-bonds in BS clusters

(Figure 8) signposts the assumption that these bonds involveelectronegative atoms from the hydrophilic heads. Afteradditional analysis of the H-bond donors and acceptors, it isfound that almost all possible combinations appear. It isnoteworthy that the peptide amino group often participates,binding either with atoms from the hydrophilic head or fromthe hydroxyl groups attached to the steroid part of aneighboring molecule. Its absence in CH and DCH may bethe reason for the lack of hydrogen bonding there. This varietyof H-bonds in the micelles of the conjugates is an additionalcorroboration of the idea of intensive dynamics of the clusteredmolecules allowing a multitude of feasible conformations. Onthe other hand, the broader distributions of the glycoconjugates (2 or 3 most probable bonds and up to 8 H-bonds in total in some clusters) may explain their fasteraggregation and higher aggregation numbers.To evaluate the influence of hydrogen bonding as a

stabilizing factor for the aggregates, the total lifetime of thevarious hydrogen bonds formed within 30 ns of the trajectoryof a given aggregate is calculated for the two nonconjugatedand for the two glyco derivatives. The total lifetime is theoverall time for which a certain hydrogen bond exists in theanalyzed part of the MD trajectory. The graphs (Figure 10)illustrate clearly the difference between CH/DCH, on onehand, and GCH/GDCH, on the other hand. In the micelles of

Figure 8. Probability of formation of different numbers of hydrogen bonds within the aggregates of GCH (hexamer), GDCH (octamer), TCH(pentamer), and TDCH (pentamer) for a period of 30 ns; the population data are normalized per molecule and per picosecond. No values areshown for the nonconjugated molecules because they practically do not form such hydrogen bonds (Table 2).

Table 2. Average Number (with Standard Deviation) andMost Probable Length of BS−BS and BS−Water HydrogenBonds (HBs) Formed by One BS Molecule in the Aggregates

molecule Naggcalc

no. of BS−BSHBs length, nm

no. BS−waterHBs length, nm

CH 5 0.08 ± 0.13 0.17 15 ± 1 0.18DCH 5 0.06 ± 0.11 0.18 13 ± 1 0.18GCH 6 0.33 ± 0.23 0.17 16 ± 1 0.18GDCH 8 0.28 ± 0.19 0.18 14 ± 1 0.18TCH 5 0.28 ± 0.26 0.19 17 ± 1 0.19TDCH 5 0.33 ± 0.24 0.19 14 ± 1 0.19

Figure 9. Illustration of the micellar structure on the example of aGCH hexamer. The hydrocarbon skeleton is colored green, the oxygenatoms red, and the nitrogen atoms blue.



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the nonconjugated salts there are 138 different H-bonds in thepentamer of CH and 90 bonds in that of DCH, whereas thesenumbers are 261 for the hexamer of GCH and 302 for theoctamer of GDCH. These much more abundant hydrogenbonds in the micelles of GCH and GDCH cannot be due onlyto the slightly larger number of molecules therein. On average,the lifetimes are also longer in the aggregates of the glycoconjugates than in those of CH and DCH.This qualitative difference between the two types of

molecules comes from the presence of the additional donorin the glyco derivatives: the peptide group, which takes part inmany hydrogen bonds (47% for GCH), mostly with protonsfrom the steroid hydroxyl groups. Having in mind thathydrogen bonding is longer-range than van der Waalsinteractions, this preference for hydrogen bonding can explainthe faster aggregation of the glyco derivatives compared to thatof nonconjugated molecules where H-bonds are virtuallymissing.

The distributions of H-bond lengths are given in Figure 11. Itis interesting that the most populated length of hydrogen bondsbetween all types of BS molecules varies in a narrow range:0.17−0.19 nm. The shorter bonds (around 0.17 nm) arecharacteristic for the glyco conjugates, and the longer ones(around 0.19 nm) are characteristic for the tauro derivatives,which is another dissimilarity resulting from the two differentheads. It should be due to the bulkier sulfate group of taurine.The fact that the H-bonds of the glyco conjugates are strongercontributes definitely to their larger aggregation numbers (6and 8) and faster self-assembly.Nevertheless, overall the intra-aggregate hydrogen bonds are

not abundant and are broken ferquently.The H-bonds between BS and water, on the other hand, are

much bigger in number, 14−17 per BS molecule (Table 2), andit fluctuates slightly around a constant average value. Thismeans that the salts always form strong hydrogen bonds withthe surrounding water molecules. The most populated H-bondlengths are the same as those within the aggregates, which

Figure 10. Total lifetimes of the various H-bonds existing during 30 ns of the trajectory of the representative clusters of CH, DCH, GCH, andGDCH; every hydrogen bond index corresponds to a different triplet donor−H−acceptor.

Figure 11. Distributions of the lengths of intracluster hydrogen bonds for the 30 ns taken from the trajectory of the representative aggregates:pentamers of TCH and TDCH, hexamer of GCH, and octamer of GDCH. The data are normalized per BS molecule.



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indicates that these distances are typical for bile salts. Hence,such a length can be expected also for H-bonds in thesecondary micelles, which are widely discussed in theliterature.3,41

The formation of a few intermolecular hydrogen bondsbetween BS and the small aggregation numbers registered inthe present study indicate that the observed aggregatescorrespond to the so-called primary micelles. This is due tothe very low concentration, on one hand, and to the limitedsimulation time, on the other. However, it does not impede theextraction of valuable information from the atomistic study.Small and co-workers3 have tested experimentally the

presence of hydrogen bonds in BS micelles by adding 4 and6 M urea, a known H-bond breaker, to micellar solutions ofvarious bile salts with different aggregation numbers. They haveestablished that the typically higher aggregation numbers ofdihydroxy salts decreased substantially (from 63 to 6 forGDCH). Nagg of the trihydroxy derivatives also decreased(down to 2). These results demonstrate that hydrogen bondsmay be important for stabilization of the aggregates. However,it should be stressed that urea is known to break thehydrophobic interactions as well, because the latter also havetheir origin in the hydrogen bonds between water molecules.44

Intermolecular Hydrophobic Interactions within theMicelles. The predominant hypothesis in the literature withrespect to stabilizing forces in bile salts aggregates is that theyare hydrophobic.4 To check this, quantitative analysis of theseinteractions was made for the most stable aggregates of the sixBS. The minimum interatomic distances (up to a cutoff of 0.60nm) between all pairs of molecules constituting a cluster weredetermined, which permitted quantitative assessment of thehydrophobic intermolecular coupling. The results are given ashistograms in Figure 12.In each analyzed aggregate the most populated minimum

distance is 0.22 or 0.23 nm, with the more probable valuesspanning the range from 0.19 to 0.26 nm. These distances areof the order of the sum (0.24 nm) of the van der Waals radii oftwo hydrogen atoms. This shows that the BS molecules in themicelles are tightly packed and form a hydrophobic mediumwhere no water molecules penetrate. It is important to notethat the population of the minimum distances, which reflectsthe number of intermolecular contacts (Table 3), is much lowerfor the tauro conjugates than for the unconjugated salts. Thedifference is spectacular for TCH. The analysis of intraclusterH-bonds for this molecule also showed that they are the fewestat the expense of the more abundant H-bonds with the watermolecules. All these factors outline the micelles of TCH as themost labile among the studied systems. TDCH is in an

intermediate position because its aggregates are moderatelystabilized by hydrophobic interactions and by intracluster H-bonds.From a comparison of the distributions of the number of

hydrogen bonds between BS molecules, which is from 0 to 1per molecule (Table 2), and the number of contacts betweenthe hydrophobic residues of the aggregated molecules, whichare in the range 300−1500 per molecule (Table 3), it can beconcluded that the stabilizing forces acting between themolecules in the BS micelles are the hydrophobic ones. Thisconclusion is in accordance with literature data and hypothesesthat hydrophobic interactions dominate the self-assemblyprocess of bile salts in diluted aqueous solutions.4,18

For the initial stage of the aggregation process, which istackled within this study, namely, the formation of primarymicelles, the intermolecular hydrogen bonds can be regardedonly as a kinetic driving force for faster aggregation of the glycoand tauro conjugated derivatives.Bearing in mind the lack of preferred intermolecular

orientation in the micelles, the fast molecular dynamics therein,the hydrophobic core, and the fact that the molecules arecoupled mainly by the soft dispersive interactions, thepronounced capacity of these aggregates for solubilization ofliophilic substances could be explained by their readiness toreadjust given an appropriate hydrophobic guest molecule.

Size and Shape of the Aggregates. Among the mostoften discussed characteristics of BS micelles for manyyears4,5,16−18 are their size and shape. As described in theIntroduction, a number of hypotheses have been formulatedabout the most probable shape and the likely size, based ondifferent experimental and theoretical data. However, there isno clear picture on the subject to date. It is known that BSaggregates are fairly different from the micelles of conventionalsurfactants and that their shape depends on the concentration

Figure 12. Distributions of the minimum distances between all pairs of molecules in the pentamers of CH, DCH, TCH, and TDCH; the hexamer ofGCH; and the octamer of GDCH. All data are normalized per one molecule and per one picosecond.

Table 3. Number of Contacts (with Standard Deviation) andMost Probable Intermolecular Separation between theAggregated BS Molecules, Averaged over the 30 ns Takenfrom the Trajectory of the Representative Clusters

molecule Naggcalc no. of contacts per molecule most probable separation, Å

CH 5 753 ± 64 2.2DCH 5 729 ± 61 2.2GCH 6 1584 ± 209 2.1GDCH 8 1035 ± 55 2.2TCH 5 264 ± 82 2.2TDCH 5 1137 ± 220 2.1



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of the bile salts and on the experimental conditions, such astemperature, pH, or ionic strength.To define the shape of the micelles, the ratios between the

moments of inertia were used in the present study, and theradius of gyration (Rg) served as a measure of the size. Theevolution of Rg along the trajectory of the representativeaggregates is shown in Figure 13.

It is evident that after a short relaxation of the clusters for ca.2 ns, which serve for intracluster reorganization, the radius ofgyration of all micelles starts fluctuating around a constantaverage value. The fluctuations are somewhat more expressedfor the conjugated derivatives than for CH and DCH, which isdue to the longer hydrophilic heads located in water, but ingeneral, all values span similar ranges. Long-time fluctuations ofRg are visible, in line with the dynamic structure of the clusters.The average sizes of the BS micelles (Table 4) are very small:

the radii are close to 1 nm. The pentamers of CH and DCHhave identical size. Rg values of the pentamers of TCH andTDCH are also similar and larger than those of thenonconjugated clusters. The hexamer of GCH is as large asthe pentamer of TCH, which is most likely due to the smallersize of the glycine residue. Expectedly, the octamer of GDCH isthe largest (Table 4). In spite of the small differences for thevarious BS, the radii of their micelles vary in a very narrowrange, 0.76−0.95 nm, which stems from the similar dimensionsof the constituting molecules. The experimentally determinedradius in the work of Woodford et al.7 of 1 nm for TCHmicelles with aggregation number 5 falls very close to thisrange. Similar small sizes have been obtained also for aggregatesof TDCH (1−1.2 nm) with Nagg = 22 (secondary micelles) byultracentrifugation and gel filtration,5,6 which indicates that ourmodel systems are a good representation of the real ones.To verify further the obtained numerical results, we

conducted an experiment to measure the size of TDCHaggregates with dynamic laser light scattering (DLS). Samples

of TDCH with concentration 100, 50, and 25 mM in 120 mMNaCl were measured, since concentration of 10 mM is belowthe apparatus sensitivity. Even the solutions with 10 timeshigher concentration gave rise to very weak signals, whichshows that the sizes are below 2 nm (the sensitivity threshold ofthe machine). This result confirms the outcome from thesimulations.The moments-of-inertia ratios are interpreted in general as

follows: Ix/Iy ≈ 1 and Iy/Iz ≈ 1 correspond to spherical shape;when Ix/Iy ≈ 1 and Iy/Iz ≪1, the shape is disc-like. In the casesIx/Iy ≪ 1 and Iy/Iz ≈ 1, the micelles are rod-like. In the studiedsystems the former ratio is close to 0.7, and the latter is about0.9. These ratios indicate that BS micelles can be modeled asellipsoids or deformed spheres, which is confirmed also byvisual inspection of the MD trajectories. This is in closeagreement with previous findings about the shape of BSmicelles.17,18

The registered specificity of all BS micelles, very small sizeand irregular shape (deformed sphere or ellipsoid), may beexplained with the ability of the BS molecules to pack whilebeing oriented in various ways with respect to each other. Thisis enabled by their special “two-faced” chemical structure. Asalready mentioned, this flexibility of orientation probablyfacilitates the solubilization of hydrophobic molecules in vivo.The present detailed analysis at the atomistic level confirms thehypothesis of Verde and Frenkel18 who state the same on thebasis of coarse-grained MD simulations of BS aggregation.

■ CONCLUSIONS

Fully atomistic molecular dynamics simulations of theaggregation process of six bile salts, encountered in humanorganisms, are carried out under conditions mimicking those inthe human gastrointestinal tract. The modeled molecules differin the number of hydroxyl groups (two or three) in the steroidskeleton and in the type of their hydrophilic head. Allsimulations are in aqueous solution, at 37 °C, in the presenceof 120 mM NaCl with concentration of the bile salts 10 mMwhich is the physiological range found in humans. Smallprimary micelles are formed in all systems on the time scale of6−110 ns. These micelles have radii about 1 nm andaggregation numbers between 5 for nonconjugated and tauroconjugated cholate and deoxycholate, and 6−8 for glycoconjugates. The bile salts aggregates are stabilized byhydrophobic interactions between the steroid rings, whereasintermolecular hydrogen bonds are few and do not affectsubstantially the stability of the primary micelles. Theintermolecular hydrogen bonds serve, however, to speed upthe aggregation of conjugated bile salts. The reason for thefaster self-assembly of taurodeoxycholate, glycodeoxycholate,and glycocholate is the formation of intracluster hydrogen

Figure 13. Evolution of the radius of gyration of the most stableaggregates of the six bile salts along their trajectory: CH, DCH, TCH,TDCH pentamer; GCH, hexamer; GDCH, octamer.

Table 4. Average Radii of Gyration (Rg’s) and Ratios of Moments of Inertia (Ij) along the Three Spatial Directions for AllRepresentative BS Aggregates

molecule Naggcalc Rg, nm Ix/Iy Iy/Iz Ix/Iz

CH 5 0.76 ± 0.03 0.72 ± 0.13 0.87 ± 0.06 0.62 ± 0.10DCH 5 0.76 ± 0.02 0.72 ± 0.12 0.88 ± 0.06 0.63 ± 0.09GCH 6 0.87 ± 0.03 0.67 ± 0.13 0.88 ± 0.06 0.58 ± 0.10GDCH 8 0.95 ± 0.03 0.77 ± 0.12 0.87 ± 0.06 0.60 ± 0.10TCH 5 0.87 ± 0.03 0.70 ± 0.12 0.84 ± 0.06 0.59 ± 0.09TDCH 5 0.85 ± 0.04 0.71 ± 0.12 0.86 ± 0.07 0.61 ± 0.09



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bonds, involving the nitrogen atom from the hydrophilic headand a proton from another molecule.The molecules within the aggregates are very dynamic; the

micelles core is entirely hydrophobic and does not tolerateinclusion of water molecules. These features of aggregates maybe considered important for the profound capacity of bile saltsmicelles to solubilize hydrophobic molecules, such ascholesterol, fatty acids, and alkylmonoglycerides in vivo.All aggregates have irregular shapes, which can be

approximated as ellipsoids or deformed spheres. Glycoconjugates yield the largest micelles (a hexamer and anoctamer) while pentamers are characteristic for the non-conjugated salts and for the tauro conjugates. The obtainedtheoretical estimates are in very good agreement withexperimental data and provide new important insights intothe bile salts aggregation mechanism and its specifics.

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.jpcb.5b07063.

Additional figures, including illustrations of molecularmodels, structures, and kinetic data, and additional tables,with force field parameters, RESP atomic charges, atomicconnectivity information, and atom types (PDF)

■ AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected]. Phone: ++35928161520.Fax: ++35929625438.NotesThe authors declare no competing financial interest.

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